In 1961, Tom Murphy's play A Whistle in the Dark appeared on the London stage, having been rejected by Dublin's Abbey Theatre. The play showed for the first time the underbelly of Irish emigration to England, displaying the violence at the heart of the Carney family, newly arrived from Ireland, as well as the futile longing for a peaceful life of the eldest son, Michael, as he tries to evade the ferocious derision and contempt of his father and brothers. The play reveals the sense of humiliation and displacement felt by the fighting, drinking Carneys in a country where they would never feel at home.

Between 1951 and 1961 more than 400,000 people – a sixth of the population – left Ireland. Two-thirds of them went to the UK, attracted by the postwar reconstruction boom and the welfare state put in place by Clement Attlee's Labour government. They were leaving a country with high unemployment, especially in rural areas, rigid Catholic church control over sexual behaviour, and poor marriage prospects for young people. London, Birmingham and Coventry offered a new life, but the sense of unchosen exile haunted many emigrants.

Anna May Mangan's memoir, Me and Mine, is an affectionate account of her parents and their siblings, who emigrated from Ireland during the 1950s, settled in London, and married, worked, had children and died there. She charts the difficulties experienced by immigrants then – "No Blacks, No Irish, No Dogs" – and their determination to both fulfil and rise above the role of "Irish peasant", an insult hurled at them on many occasions. When her father flew home for a funeral in the early 60s, his first time on a plane, the stewardess asked if he wanted a drink from the trolley, and he politely requested a pint of stout. She hissed: "This is not a pub, you Irish peasant."

Like many Irish emigrant families, Mangan's remained close: her relatives socialised together at various dancehalls and pubs in Cricklewood, and her mother's sisters were constantly in and out of each other's houses. Big occasions such as weddings and funerals were attended by large numbers of people. Mangan had a ghoulish Aunt Winifred, who longed for funerals and the inevitable benefit dances held to raise money to pay for them. She had high standards in terms of the quality of the religious service and the hospitality offered, and would frequently berate the bereaved for shortcomings in either department.

Four of Mangan's aunts died young of cancer, and she, her sister and her mother survived early onset of the disease. The value of early diagnosis is poignantly underlined, with various fears and superstitions taking the place of medical consultation: her aunts believed that cutting into a cancerous tumour would inevitably spread it, and thus avoided doctors until matters were well advanced. Mangan is very good on the shame that accompanied cancer then, particularly breast or ovarian cancer, which her aunts could not talk about without extreme embarrassment.

The book deals with food in great detail, from the turkeys sent by an aunt in Ireland every Christmas by boat and train – they were maggot-infested by the time they arrived – to the delicious cakes competitively baked by her London aunts, to the pot luck taken by the family each evening when her father worked for Heinz and used to bring home large quantities of unlabelled cans; you might get beef stew, rice pudding or baked beans, and you had to eat whichever it was. Each day her mother fed a cantankerous lady tenant downstairs from their flat, who took it for granted that she would receive free food and never thanked anyone for it.

The joys and sorrows of a large working-class Irish emigrant family are amply and honestly covered, including shocking casual domestic violence. It is clear that Mangan holds her extended family in great affection, but there are some strange gaps in the narrative. We never find out precisely where in Ireland her parents came from, even though Mangan spent six weeks every year on holiday with her Irish relatives. It is very unusual for Irish emigrants to forget or suppress where they come from; they generally preserve a pronounced sense of "the home place". There is one hint, far into the book, of Westmeath as a possible location, but that's all.

Ireland is not a homogeneous place: Donegal is as different from Wexford as Yorkshire is from Cornwall, and there are distinct differences within counties even down to parish level. Mangan's relatives are slightly too Irish-generic, in spite of her attention to their individual quirks. There is a kind of hollowness to the statement made by her father – "Remember we're just visitors in this country" – when the potential destination of family return is never named. The exoticism of red lemonade and the stickiness of cow dung are mentioned when Mangan has her annual holidays in Ireland, but there's no rich local detail of the sort that characterises real places like John McGahern's Leitrim, John B Keane's Kerry or Brian Friel's Donegal. Martin McDonagh got six plays out of his annual holidays in Galway and has created a whole new version of the west of Ireland.

Despite its topographical vagueness, Me and Mine is, as its subtitle proclaims, warm-hearted, and Mangan has captured many memorable characters whose lives deserve to be recorded.